Achieving fast convergence on an energy-limited and computationally-constrained platform still remains a dream in spite of magnificent advancements in Integrated Circuit (IC) technologies. For instance, in telephony, the echo cancellation re quires a high-definition adaptive-filtering algorithm that further needs a robust convergence performance while tracking the time varying uncertainties present in the communication link. Nevertheless, such high definition adaptive algorithm cannot be run on an energy-limited and computationally-constrained inexpensive platform. The research work in this thesis focuses to propose the low-complexity distributed adaptive filtering solution for energy-constrained platforms. The thesis is orga nized in three parts. Part-1 aims to develop a low-complexity MIMO channel estimation algorithm for MIMO communication system. Part-II and III pro vide the distributed and diffusion based adaptive signal processing solutions for computationally-constrained inexpensive platforms. The thesis begins with an overview of the adaptive algorithms with implementa tion constraints and then proceeds towards a comprehensive and detailed literature survey. The literature survey can be classified into two major areas, i.e. adaptive filter theory and adaptive algorithm implementation over low-cost platforms. Fur thermore, a channel model is presented with the consideration of two multipath components for MIMO communication environment. Taking it as a reference as channel model, a spatiotemporal low-complexity adaptive estimation algorithm is proposed by assuming time-variant block fading channel with fixed number of training symbols. The proposed algorithm exhibits better results than those shown by some notable least square algorithms in the literature. The effect of varying doppler rates on the convergence performance of the algorithm is thoroughly ob served to check the validation of the algorithm. Obtained simulated results show that the proposed algorithm entails low-complexity and provides independency on forgetting factor as compared to notable adaptive filtering algorithms. x In the second part of the thesis, a novel processing-efficient architecture of a group of inexpensive and computationally-constrained small platforms is proposed for a parallely-distributed adaptive signal processing (PDASP) operation. The pro posed architecture is capable of running computationally-expensive procedures like complex adaptive algorithms cooperatively. The proposed PDASP architecture operates properly even if perfect time alignment among the participating plat forms is not available. Complexity and processing time of the PDASP scheme are compared with those of the sequentially-operated algorithms. The comparative analysis shows that the PDASP scheme exhibits much lesser computational com plexity parallely than the sequentially-operated algorithms. Moreover, for high and low doppler rates, the proposed architecture provides a parallely-decreased processing time than the sequentially-operated MIMO algorithms. In part III, a novel distributed diffusion-based adaptive signal processing (DDASP) architecture for computationally-constrained small platforms is introduced. In the proposed DDASP architecture, the adaptive algorithm is diffused into the desired number of processing devices. The number of processing nodes that are used in DDASP architecture is dependent upon the number of MIMO channel streams as well as on the number multipath components. Therefore, having more nodes and diffusion mechanism, the proposed DDASP architecture exhibits lesser and linear computational complexity parallely on each processing node involved as compared to the proposed PDASP architecture.